
on Econometric Time Series 
By:  Tobias Hartl; Roland Weigand 
Abstract:  We propose convenient inferential methods for potentially nonstationary multivariate unobserved components models with fractional integration and cointegration. Based on finiteorder ARMA approximations in the state space representation, maximum likelihood estimation can make use of the EM algorithm and related techniques. The approximation outperforms the frequently used autoregressive or moving average truncation, both in terms of computational costs and with respect to approximation quality. Monte Carlo simulations reveal good estimation properties of the proposed methods for processes of different complexity and dimension. 
Date:  2018–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1812.09142&r=all 
By:  Delle Monache, Davide (Bank of Italy); Petrella, Ivan (University of Warwick and CEPR) 
Abstract:  In this work we explore a novel approach to estimating Gaussian state space models in the classical framework without making use of the Kalman filter and Kalman smoother. By formulating the model in matrix form, we obtain expressions for the likelihood function and the smoothed state vector that are computationally feasible and generally more efficient than the standard filtering approach. Finally, we highlight a convenient way to retrieve the filtering weights and to deal with data irregularities. 
Keywords:  State space models; Likelihood; Smoother; Sparse matrices; JEL Classification Numbers: C22 ; C32 ; C51 ; C53; C82; 
Date:  2019 
URL:  http://d.repec.org/n?u=RePEc:wrk:wrkemf:19&r=all 
By:  Hauzenberger, Niko; Huber, Florian 
Abstract:  In this paper we aim to improve existing empirical exchange rate models by accounting for uncertainty with respect to the underlying structural representation. Within a flexible Bayesian nonlinear time series framework, our modeling approach assumes that different regimes are characterized by commonly used structural exchange rate models, with their evolution being driven by a Markov process. We assume a timevarying transition probability matrix with transition probabilities depending on a measure of the monetary policy stance of the central bank at the home and foreign country. We apply this model to a set of eight exchange rates against the US dollar. In a forecasting exercise, we show that model evidence varies over time and a model approach that takes this empirical evidence seriously yields improvements in accuracy of density forecasts for most currency pairs considered. 
Keywords:  Empirical exchange rate models, exchange rate fundamentals, Markov switching 
Date:  2018–12 
URL:  http://d.repec.org/n?u=RePEc:wiw:wus005:6770&r=all 
By:  Tobias Hartl; Roland Weigand 
Abstract:  We investigate a setup for fractionally cointegrated time series which is formulated in terms of latent integrated and shortmemory components. It accommodates nonstationary processes with different fractional orders and cointegration of different strengths and is applicable in highdimensional settings. In an application to realized covariance matrices, we find that orthogonal short and longmemory components provide a reasonable fit and competitive outofsample performance compared to several competitor methods. 
Date:  2018–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1812.09149&r=all 
By:  Davy Paindaveine; Julien Remy; Thomas Verdebout 
Abstract:  We consider inference on the first principal direction of a p variate elliptical distribution. We do so in challenging double asymptotic scenarios for which this direction eventually fails to be identifiable. In order to achieve robustness not only with respect to such weak identifiability but also with respect to heavy tails, we focus on signbased statistical procedures, that is, on procedures that involve the observations only through their direction from the center of the distribution. We actually consider the generic problem of testing the null hypothesis that the first principal direction coincides with a given direction of R p. We first focus on weak identifiability setups involving single spikes (that is, involving spectra for which the smallest eigenvalue has multiplicity p1). We show that, irrespective of the degree of weak identifiability, such setups offer local alternatives for which the corresponding sequence of statistical experiments converges in the Le Cam sense. Interestingly, the limiting experiments depend on the degree of weak identifiability. We exploit this convergence result to build optimal sign tests for the problem considered. In classical asymptotic scenarios where the spectrum is fixed, these tests are shown to be asymptotically equivalent to the signbased likelihood ratio tests available in the literature. Unlike the latter, however, the proposed sign tests are robust to arbitrarily weak identifiability. We show that our tests meet the asymptotic level constraint irrespective of the structure of the spectrum, hence also in possibly multispike setups. Finally, we fully characterize the nonnullasymptotic distributions of the corresponding test statistics under weak identifiability, which allows us to quantify the corresponding local asymptotic powers. Monte Carlo exercises confirm our asymptotic results. 
Keywords:  Le Cam's asymptotic theory of statistical experiments, Local asymptotic normality, Principal component analysis, Sign tests, Weak identi ability. 
Date:  2019–01 
URL:  http://d.repec.org/n?u=RePEc:eca:wpaper:2013/280742&r=all 
By:  Corrado, L.; Stengos, T.; Weeks, M.; Ege Yazgan, M. 
Abstract:  In many applications common in testing for convergence the number of crosssectional units is large and the number of time periods are few. In these situations asymptotic tests based on an omnibus null hypothesis are characterised by a number of problems. In this paper we propose a multiple pairwise comparisons method based on an a recursive bootstrap to test for convergence with no prior information on the composition of convergence clubs. Monte Carlo simulations suggest that our bootstrapbased test performs well to correctly identify convergence clubs when compared with other similar tests that rely on asymptotic arguments. Across a potentially large number of regions, using both crosscountry and regional data for the European Union we find that the size distortion which afflicts standard tests and results in a bias towards finnding less convergence, is ameliorated when we utilise our bootstrap test. 
Keywords:  Multivariate stationarity, bootstrap tests, regional convergence. 
JEL:  C51 R11 R15 
Date:  2018–12–21 
URL:  http://d.repec.org/n?u=RePEc:cam:camdae:1873&r=all 
By:  Gabriele Fiorentini (Università di Firenze, Italy; Rimini Centre for Economic Analysis); Enrique Sentana (CEMFI, Spain) 
Abstract:  We propose tests for smooth but persistent serial correlation in risk premia and volatilities that exploit the nonnormality of financial returns. Our parametric tests are robust to distributional misspecification, while our semiparametric tests are as powerful as if we knew the true return distribution. Local power analyses confirm their gains over existing methods, while Monte Carlo exercises assess their finite sample reliability. We apply our tests to quarterly returns on the five FamaFrench factors for international stocks, whose distributions are mostly symmetric and fattailed. Our results highlight noticeable differences across regions and factors and confirm the fragility of Gaussian tests. 
Keywords:  financial forecasting, moment tests, misspecification, robustness, volatility 
JEL:  C12 C22 G17 
Date:  2019–01 
URL:  http://d.repec.org/n?u=RePEc:rim:rimwps:1901&r=all 
By:  Pavel Ciaian; d'Artis Kancs; Miroslava Rajcaniova 
Abstract:  This is the first paper that estimates the price determinants of BitCoin in a Generalised Autoregressive Conditional Heteroscedasticity framework using high frequency data. Derived from a theoretical model, we estimate BitCoin transaction demand and speculative demand equations in a GARCH framework using hourly data for the period 20132018. In line with the theoretical model, our empirical results confirm that both the BitCoin transaction demand and speculative demand have a statistically significant impact on the BitCoin price formation. The BitCoin price responds negatively to the BitCoin velocity, whereas positive shocks to the BitCoin stock, interest rate and the size of the BitCoin economy exercise an upward pressure on the BitCoin price. 
Date:  2018–12 
URL:  http://d.repec.org/n?u=RePEc:arx:papers:1812.09452&r=all 
By:  Shaw, Charles 
Abstract:  In a recent contribution to the financial econometrics literature, Chu et al. (2017) provide the first examination of the timeseries price behaviour of the most popular cryptocurrencies. However, insufficient attention was paid to correctly diagnosing the distribution of GARCH innovations. When these data issues are controlled for, their results lack robustness and may lead to either underestimation or overestimation of future risks. The main aim of this paper therefore is to provide an improved econometric specification. Particular attention is paid to correctly diagnosing the distribution of GARCH innovations by means of Kolmogorov type nonparametric tests and Khmaladze's martingale transformation. Numerical computation is carried out by implementing a GaussKronrod quadrature. Parameters of GARCH models are estimated using maximum likelihood. For calculating Pvalues, the parametric bootstrap method is used. Further reference is made to the merits and demerits of statistical techniques presented in the related and recently published literature. 
Keywords:  Autoregressive conditional heteroskedasticity (ARCH), generalized autoregressive conditional heteroskedasticity (GARCH), market volatility, nonlinear time series, Khmaladze transform. 
JEL:  C22 C58 
Date:  2018–11–01 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:90437&r=all 
By:  Aknouche, Abdelhakim; Demmouche, Nacer; Touche, Nassim 
Abstract:  A Bayesian MCMC estimate of a periodic asymmetric power GARCH (PAPGARCH) model whose coefficients, power, and innovation distribution are periodic over time is proposed. The properties of the PAPGARCH model such as periodic ergodicity, finiteness of moments and tail behaviors of the marginal distributions are first examined. Then, a Bayesian MCMC estimate based on GriddyGibbs sampling is proposed when the distribution of the innovation of the model is standard Gaussian or standardized Student with a periodic degree of freedom. Selecting the orders and the period of the PAPGARCH model is carried out via the Deviance Information Criterion (DIC). The performance of the proposed GriddyGibbs estimate is evaluated through simulated and real data. In particular, applications to Bayesian volatility forecasting and ValueatRisk estimation for daily returns on the S&P500 index are considered. 
Keywords:  Periodic Asymmetric Power GARCH model, probability properties, GriddyGibbs estimate, Deviance Information Criterion, Bayesian forecasting, Value at Risk. 
JEL:  C11 C15 C58 
Date:  2018–05–11 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:91136&r=all 
By:  Dominik Bertsche (Department of Economics, Box 129, 78457 Konstanz, Germany); Ralf Brüggemann (Department of Economics, Box 129, 78457 Konstanz, Germany); Christian Kascha 
Abstract:  We represent the dynamic relation among variables in vector autoregressive (VAR) models as directed graphs. Based on these graphs, we identify socalled strongly connected components (SCCs). Using this graphical representation, we consider the problem of variable selection. We use the relations among the strongly connected components to select variables that need to be included in a VAR if interest is in forecasting or impulse response analysis of a given set of variables. We show that the set of selected variables from the graphical method coincides with the set of variables that is multistep causal for the variables of interest by relating the paths in the graph to the coecients of the `direct' VAR representation. Empirical applications illustrate the usefulness of the suggested approach: Including the selected variables into a small US monetary VAR is useful for impulse response analysis as it avoids the wellknown `pricepuzzle'. We also nd that including the selected variables into VARs typically improves forecasting accuracy at short horizons. 
Keywords:  Vector autoregression, Variable selection, Directed graphs, Multistep causality, Forecasting, Impulse response analysis 
JEL:  C32 C51 E52 
Date:  2018–12–10 
URL:  http://d.repec.org/n?u=RePEc:knz:dpteco:1808&r=all 
By:  Gergely Ganics (Banco de España); Atsushi Inoue (Vanderbilt University); Barbara Rossi (ICREA  Univ. Pompeu Fabra) 
Abstract:  In this paper we propose methods to construct confidence intervals for the bias of the twostage least squares estimator, and the size distortion of the associated Wald test in instrumental variables models. Importantly our framework covers the local projections — instrumental variable model as well. Unlike tests for weak instruments, whose distributions are nonstandard and depend on nuisance parameters that cannot be estimated consistently, the confidence intervals for the strength of identification are straightforward and computationally easy to calculate, as they are obtained from inverting a chisquared distribution. Furthermore, they provide more information to researchers on instrument strength than the binary decision offered by tests. Monte Carlo simulations show that the confidence intervals have good small sample coverage. We illustrate the usefulness of the proposed methods to measure the strength of identification in two empirical situations: the estimation of the intertemporal elasticity of substitution in a linearized Euler equation, and government spending multipliers. 
Keywords:  instrumental variables, weak instruments, weak identification, concentration parameter, local projections 
JEL:  C22 C52 C53 
Date:  2018–12 
URL:  http://d.repec.org/n?u=RePEc:bde:wpaper:1841&r=all 
By:  Chen, Siyan; Desiderio, Saul 
Abstract:  In this paper we present a simple approach to factor analysis to estimate the true correlations between observable variables and a single common factor. We first provide the exact formula for the correlations under the orthogonality conditions, and then we show how to consistently estimate them using a random sample and a proper instrumental variable. 
Keywords:  Factor analysis, correlation, instrumental variable estimation 
JEL:  C1 C38 
Date:  2018 
URL:  http://d.repec.org/n?u=RePEc:pra:mprapa:90426&r=all 